Models for supercontinuum generation beyond the slowly-varying-envelope approximation

Abstract

We show numerically that both the modified Korteweg-de Vries and the sine-Gordon models are conducive to the generation of supercontinua with spectral bandwidths of several octaves, when an intense short pulse is launched as the initial condition. These models beyond the slowly-varying-envelope approximation could play an important role in modeling supercontinuum generation in gas-filled hollow waveguides.

Modeling Frequency Comb Sources

“…Although it has been shown that the SVEA can be used to describe single-cycle pulse propagation and extreme spectral broadening processes such as SC generation [97,103], there are considerable ongoing theoretical works on the correction of the SVEA approach [97,104,105]. The models beyond the SVEA derived from Maxwell's equation, including the modified Korteweg-de Vries (mKdV), sine-Gordon (sG), mKdV-sG, and short pulse equation (SPE), which is recognized as a reduction of the mKdV-sG [99], have been proven effective in modeling ultrafast phenomena where the NLSE is no longer valid [98,100,106,107]. Here we only introduce the SPE, which is the simplest among those mentioned above.…”

“…The left-hand side of (9) describes the dispersion and nonlinearity and the right-hand side of (9) Figure 8 shows the evolution from a noise seed to an ultrashort pulse governed by the SPE. The SPE captures the phase dynamics of the electric field, which is important in characterizations of few-cycle to attosecond pulses [99,100,102,107] and mode-locked lasers down to few cycle or subcycle regime [98,108]. …”

Few-cycle solitons in supercontinuum generation dynamics

“…We can gain further understanding from a simple analytic approach of the third harmonic generation. Let us indeed consider the approximate solution of the mKdVsG equation given by (27) and (28). The correction term u 1 in (27) is a third harmonic…”

“…Let us consider a quasi-monochromatic wave with angular frequency ω and wave vector k, as u = U (z, t)e i(kz−ωt) + cc + u 1 (z, t), (27) where U is the amplitude of the fundamental wave, cc holds for 'complex conjugate', and u 1 is some small correction. Equation (27) neglect dispersion, and disregard third harmonic generation, which yields…”

The method of surface plasmon-polariton pulses generation via cooperative effects in waveguide spaser

“…We also demonstrate the possibility of a strong spectral broadening and generation almost rectangular spectrum SPP pulses due to the existence of a strongly nonlinear near-field effects in the dielectric layer with a dense ensemble of chromophores. However, the possibility of a SPP supercontinuum generation in the system under study requires a substantial reduction in the pulse duration and the use of novel models [3] beyond the slowly-varying-envelope approximation. The possibility of control of SPP pulse dynamic by analogous an effect of triggered superradiance [4], as well as by means of an external magnetic field using magnetic nanostructures [5] is discussed.…”